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Glauber Dynamics for Sampling Colorings: Rapid Mixing above $(1+1/\mathrm{e})Δ$ via Hidden Hard-Core Models — arXiv:2611.04699

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04699
License (as archived): CC0-1.0
Archived: 2026-11-04T21:56:25.659Z
SHA-256 of the archived text: 2e273770ae8c2954213b28035c737b8041999f64a0f3f45bec2a4e708c643678
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How to cite

Glauber Dynamics for Sampling Colorings: Rapid Mixing above $(1+1/\mathrm{e})Δ$ via Hidden Hard-Core Models — arXiv:2611.04699 — arXiv (en), https://arxiv.org/abs/2611.04699 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c837fcfbb1cd (Metraipolis archive dc_c837fcfbb1cd, sha256 2e273770ae8c2954213b28035c737b8041999f64a0f3f45bec2a4e708c643678)

BibTeX

@misc{dcc837fcfbb1cd,
  title = {Glauber Dynamics for Sampling Colorings: Rapid Mixing above $(1+1/mathrme)Δ$ via Hidden Hard-Core Models — arXiv:2611.04699},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04699},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c837fcfbb1cd; sha256 2e273770ae8c2954213b28035c737b8041999f64a0f3f45bec2a4e708c643678},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04699. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We show that for every $\gamma>0$ and every sufficiently large $\Delta$, the Glauber dynamics for proper $q$-colorings of any $n$-vertex graph of maximum degree $\Delta$ has spectral gap $\Omega_\gamma(1/n)$, and hence mixing time $O_\gamma(n^2\log q)$, whenever $q\ge(1+1/\mathrm{e}+\gamma)\Delta$. Our proof establishes a Bochner-type inequality by exploiting the spectral gaps of hard-core models hidden in the color classes. The constant $1+1/\mathrm{e}\approx1.368$ comes from the uniqueness threshold $\approx\mathrm{e}/\Delta$ of the hard-core model on the infinite $\Delta$-regular tree.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Discrete Mathematics (cs.DM); Combinatorics (math.CO); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.04699 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T21:41:04.552Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).